Hollow beam electron gun



June 28, 1966 c, 8. KING ETAL 3,258,626

HOLLOW BEAM ELECTRON GUN Filed Sept. 18, 1961 4 Sheets-Sheet l I I l WATER LINE AFTER TlLTlNG INVENTORS GORDON S. KINO NORMAN J.TAYLOR ATTORNEY June 1966 G. s. KlNO ETAL 3,258,626

HOLLOW BEAM ELECTRON GUN Filed Sept. 18, 1961 4 Sheets-Sheet 2 0 FIG. 2

FIG.3

INVENTORS GORDON S.KINO NORMAN J.TAYLOR ATTORNEY June 28, 1966 G. s. KINO ETAL 3,258,6 6

HOLLOW BEAM ELECTRON GUN Filed Sept. 18, 1961 4 Sheets-Sheet 3 FIG-.4

INVENTORS GORDON S. KINO NORMAN J.TAYLOR Ai'TORNEY June 1956 G. 5. KING ETAL 3,258,626

HOLLOW BEAM ELECTRON GUN Filed Sept. 18, 1961 4 Sheets-Sheet 4 FIG.IO

INVENTORS GORDON S.KINO NORMAN J. TAYLOR BYWAZ% TTORNEY United States Patent 3,258,626 HOLLOW BEAM ELECTRQN GUN Gordon S. Kine, Palo Alto, and Norman .1. Taylor, Sunnyvale, Calif, assignors to Varian Associates, Palo Alto, Calif., a corporation of California Filed Sept. 18, 1961, Ser. No. 138,856 29 Claims. (Cl. 31382) This invention relates in general to electron guns and, more particularly, to an electron gun that produces a hollow beam.

A hollow electron beam, that a beam in which the electrons form an annular cross section, is well known in the art and has many advantages over a solid electron beam including less electron potential spread radially across the beam than a solid beam of the same outside diameter carrying the same current. As a result, hollow beams may be pushed to higher perveances than solid beams before the formation of virtual cathodes. Then at perveances well below the limiting value, the hollow confined-flow beam will have less velocity spread between electrons, than its solid counterpart of the same perveance. In the case of both Brillouin and confined focused-flow, a lower drift tube potential can be used with a hollow beam for a given D.C. beam power. In addition, since a larger proportion of the beam electrons can be acted upon by the strongest region of the high frequency fields of a particular circuit, a hollow beam interacts more efficiently than a solid beam with high frequency circuits. Furthermore, the emission surface of hollow beam electron guns is not usually subjected to bombardment by positive ions created by the primary beam since these positive ions tend to travel along the electron tube laxis where there is no emission surface. At the same time, there is little bombardment of the cathode by secondary electrons resulting from interception of primary electrons by the drift tube, collector, etc., since these electrons tend to follow different paths from those in the primary beam, and thus are unlikely to hit a cylindrical conical or annular cathode.

In the past hollow beam have been produced by an annular emitting surface with focusing ring electrodes disposed on both the inner and outer periphery of the emitting surface. The anode usually had an annular aperture. Because of the difficulty in designing convergent hollow beam guns of this type, only beams of limited current densities can be produced. An alternative type of hollow beam gun is the magnetron injection gun which comprises either a cylindrical or conical surface cathode surrounded by either a cylindrical or conical surface anode. High current densities may be obtained from this gun, however, in a gun having a cathode length of more than one diameter a uniform cathode emission which has uniformity to within is difficult to obtain and the noise level of the gun at high voltages is relatively high.

The principal object of this invention is to produce a high density, high perveance, low noise level, hollow beam electron gun having a substantially uniform emission across the cathode.

One feature of this invention is an elongated emitting surface disposed in a predominantly radial electric field, the intensity of which varies along the axial length of the cathode whereby uniform cathode emission is obtained.

Another feature of this invention is a tubular anode concentric with a tubular elongated cathode and disposed either exterior or interior of the cathode wherein the anode has a special bell-shape forming a non-uniform electric field so that uniform emission is obtained across the cathode.

Another feature of this invention is a tubular cathode azsasze ice emission surface having uniform emission wherein its axial length is made much greater than its diameter.

Another feature of this invention is the provision of a substantially cylindrical focus electrode disposed coaxially of and in front of -a tubular cathode to help shape the fields so that uniform cathode emission is obtained.

Another feature of this invention is a frusto-conical focusing electrode disposed at an angle with a tubular cathode which angle is preferably equal to a value between and 157.5".

These and other features and advantages of the present invention will .be more apparent after a perusal of the following specification taken in connection with the accompanying drawings wherein,

FIG. 1 is an axial cross section of the novel :axisymmetrical electron gun as installed within a suitable vacuum envelope,

FIGS. 2, 3, 4 and 5 are graphs of normalized values of equipotential lines plotted on a normalized Y-Z co-ordinate system for angles of 2, 4, 6 and 8 respectively that the magnetic field makes with the cathode emission surface,

FIG. 6 is a plan view of an electrolytic tank showing models of the electrodes of a planar gun,

FIG. 7 is a pictorial view of an electrolytic tank showing models of the electrodes to simulate an axisymmetrical gun,

FIG. 8 is a schematic line drawing of the novel electron FIG. 9 illustrates an alternate embodiment for the inner focusing electrode of the gun shown in FIG. 1,

, H68. 10 and 11 illustrate two possible alternate embodiments for the anode, and

FIG. 12 illustrates a schematic embodiment of an inside out gun incorporating the invention.

Referring to FIG. 1 of the drawings, the hollow beam axisymmetrical electron gun includes preferably a frustoconical em'itting surface 11 having a cone apex angle equal to 8 although a cone apex angle of as large as 20 or smaller than 2 are feasible values. A cylindrical front inner focusing electrode 12 having a diameter slightly larger than the smallest cathode diameter is disposed at the smaller diameter end or the front end of the surface 11. At the larger diameter end or the rear of the cathode, a frusto-conical focusing electrode 13 is disposed and has a cone apex angle of approximately 98 and, therefore, the angle between an element on the cathode and an element on the electrode 13, which elements are both in the same plane, form an angle equal to 135. The angle formed by the cathode and the focusing electrode 13 may be as small as 115 and as large as The emitting surface 11 in this embodiment is machined on a tubular matrix member 14, usually comprising a porous metal such as tungsten, in which is embedded a good electron emitter such as a mixture of barium and strontium oxides. Other types of cathodes such as an oxide coated surface formed on a sheet metal base of nickel can be used in placed of the matrix member 14. The matrix member 14 is mounted on three sapphire rods 16 spaced about the axis which rods are in turn axially mounted between two center-apertured axially aligned ceramic disks 17 and 18 brazed at their apertures to a'thin-wall metallic support tube 1Q. A noninductive helical cathode heater coil 21 is positioned within and against the sapphire rods 16 between the disks 17 and 18, and suitable electrical leads 22 and 23 (shown schematically) supply electric energy to the heater coil 21. Since the coil 21 is next to the sapphire rods 16, it does not need to be insulated as it would need to be if the sapphire rods were not used.

The cylindrical focusing electrode 12 is mounted onto the thin-wall tube 19 with the aid of a metal plug 24 brazed 'at one end of the tube 19. The metal plug 24 has a protruding flange 26 through which is disposed axially aligned small spacer pins 27. The opposite ends of pins 27 bear between the ceramic disk 17 and a header 28 on the focusing electrode 12. On the other side of header 28, a suitable snap-ring 29 that is disposed between a circumferential groove 31 on plug 24 and on internal circumferential groove 32 on electrode 12 secures the electrode 12 accurately with respect to the cathode 14 and coaxial thereto. The potential of electrode 12 is preferably maintained at cathode potential but since the two are insulated from each other the electrode 12 can be maintained at a biased potential different than the cathode by means of a lead passing through tube 19.

The other ceramic disk 18 is coaxially secured on the forward projetcing end of an internal flange 33 on a tubular metallic cathode support 34 by means of a plurality of bent metal straps 35. The conical focusing electrode 13 is also mounted onto the flange 33 at the outer periphery thereof and held in place by suitable bolts 36 counterbored into the electrode 13 so that no protrusions are formed in the conical surface thereof. Both focusing electrodes 12 and 13 are spaced from the cathode 14 so that very little heat is conducted to the electrodes 12 and 13 and the electrodes are thus maintained at a temperature below their electron emission temperature. Cathode potential is supplied to the cathode 14 through the metal straps 35 which contact a short, metal sleeve 38 that is positioned around the sapphire rods 16 and fits into an annular recess in the larger diameter end of the cathode 14. A bell-shape anode 39 is disposed concentric with the emitting surface 11 and focusing electrodes 12 and 13, with the larger diameter portion of the bell-shaped anode 39 positioned around the larger diameter end of the emitting surface 11. The word bellshaped will be defined hereinafter.

The components of the electron gun are disposed preferably within an axially parallel magnetic field, represented by arrow B (which also represents the axis of the gun about which the gun is symmetrical) wherein the magnetic field B in this embodiment is directed in the direction that the electron beam fiows. Since the surface 11 is conical and as mentioned above has an apex angle of 8", the magnetic field forms a small angle 0 with the emitting surface 11 which angle is half the cone apex angle (4) of the frusto-conical emitting surface 11. A drift tube means 41 is disposed adjacent the smaller diameter end of the bell-shaped anode 39. If the drift tube means 41 is at the same potential as the anode 39, the two can be combined into one structure.

When the cathode 14 is heated to emission temperature by the heater 21 electrons are emitted from surface 11 since there is a potential difference between the bell-shaped" anode and the cathode and also an axially parallel magnetic field, a hollow electron beam 42 will be formed and it will travel parallel to the axis of the gun. The front focusing electrode 12 determines the inside radius r of the beam which is equal to the radius a at the forward end of the cathode 14. The inner electrons are observed to leave the circumference at radius a with a radial component but the inner radius r reduces to the value a in front of the front focus electrode 12 that helps to form the field lines to obtain better uniformity of cathode emission. The outside radius of the beam r is larger than the radius b at the rear end of cathode 14 because of outwardly directed space charge forces. Since the anode must be at a positive potential with respect to the cathode and with the magnetic field as directed by arrow B the electron will follow a spiral path around the axis traveling axially from the rear of the cathode to the front and into the drift tube 41. If the direction of the arrow B was turned 180 the beam will be formed in the same manner as above but the electrons will spiral in a reverse direction but also into the drift tube 41. The bell-shape of the anode 39 allows the cathode to have uniform emission. This anode bellshape is limited to a geometry that provides a potential field which in the presence of space charge produced by the beam assumes a bell-shape. That is, the equipotential lines around the beam form tubular surfaces in which the diameter varies non-linearly along the axis, and the bell-shape equipotential surfaces have their largest diameter at the rear end of the cathode and the smallest diameter at the front end. The equations for these equipotential surfaces for special cases and how they are produced in other cases will be described hereinafter. Therefore, hereinafter, the phrase bell-shape anode refers to an anode geometry which produces the bell-shape equipotential surfaces as described above. In FIG. 1, since the anode is also an equipotential surface, the inner surface, the surface facing the cathode was made to conform to a particular equipotential surface. Other anode structures, as will be shown hereinafter, will produce the bell-shape equipotential surfaces that in turn produce a uniform emission from the cathode.

The axial cross-section bell-shape of the anode of FIG. 1 of axisymmetrical design is approximated as follows: The anode shape or the equipotential lines in the presence of space charge of a gun of planar form should be determined by first assuming a planar cathode surface to lie in the x-z plane of an orthogonal x-y-z co-ordinate system. The length of the cathode in the x direction is infinite. The magnetic field has a component directed in the z direction and also has a smaller component in the y direction whereby the resultant magnetic field makes an angle 9 with the cathode surface as it passes therethrough. The resultant magnetic field may point towards or away from the cathode. An electron emitted from the cathode thus travels in the positive z and y direction (it also has a velocity component in the x direction since it crosses the magnetic field). The equipotential lines in the presence of space charge in the y-z plane from which lines the electrodes for the planar gun are determined are given by the following equation:

11 2 1L4 4 cos 1+ sm 0 S111 (0+ :1) (1) where I is the normalized potential value, 0 is the angle the magnetic field makes with the x-z plane, and u and at are real numbers and represent an arbitrary co-ordinate system. These arbitrary co-ordinates are converted to the Cartesian x-y-z co-ordinates by the equations:

verted to meters by using the following normalizing relationships where 1 is equal to the ratio of e//n (electron charge to electron mass),

1 is the current density at the cathode, s is a constant and is equal to 8.854 l0 farads per meter in m.k.s. unit of measure, in other unit of measure s has a different value and care must be taken that all factors are in the same unit of measure; and w is equal to 1B where B is the resultant magnetic field intensity (FIG. 1).

5 The Equations 1, 2 and 3 are in normalized form so that the terms are in a simplified form and apply to any gun one wishes to design using the teachings of this invention. The factors J w, 17 and B are constants within a given electron gun. Also Equations 1, 2 and 3 were derived from a universal beam trajectory, which produces uniform electron emission from a cathode surface.

FIGS. 2, 3, 4 and 5 respectively illustrate a series of normalized equipotential curves I in the normalized Y-Z plane for 0 angles having values of 2, 4, 6 and 8 respectively. These curves were calculated by using Equations 1, 2 and 3 and are valid for distances in the positive z direction past the end of the cathode by approximately one quarter of a cathode length. 1 Y and Z values are normalized values in that they have to be multiplied by the above normalizing Formulas 4, 5 and 6 to be converted to volts and meters. The line designated 0 in each figure corresponds to I =O and the left hand portion of this line which is located on the negative side of the y-co-ordinate axis represents the surface of the rear focusing electrode 13 of the gun. As mentioned above in an actual gun this line preferably forms an angle between 45 and 67.5 with the y axis. The right hand portion of the I =0 line which is located on the positive side of the y-co-ordinate axis represents a front focus electrode, when this focus electrode is operated at zero potential. The surface of this front focus electrode makes an angle substantially equal to 0 with the z-axis.

Curves in FIGS. 2 through 5 were plotted by assuming an infinitely short cathode in the z direction. Equations 1, 2 and 3, used to calculate curves 2-5, are only valid outside the beam. All the electrons within the beam are assumed to follow the same shaped universal beam trajectory. Consequently line 42, on the graphs, represents both the top and bottom edge of the beam. This means that the total beam trajectory for a beam of finite thickness may readily be determined, after being given any finite cathode length in the z direction, as all the beam particle trajectories have the same shape within the gun. Thus, in a sense, curves of FIGS. 25 are universal for any given cathode length when one realizes that the scale in the z direction for the region outside the beam but between the beam and the focus electrode is different than the 2 scale for the region above the beam. Below the lower beam edge the true 2 scale includes a value of Z as found in the graphs of FIGS. 2-5 plus the finite length of the given cathode in the z direction. The 2 scale reads correctly for values of I above the upper edge of the beam without correction for the finite length of the cathode.

Other values of 1 for the same 6 angle can be interpolated from the graphs, while 1 for different 0 angles can be interpolated from two or more graphs or one can calculate them using Equations 1, 2 and 3.

The electric fields and equipotential lines along the beam trajectory and thus within the beam (that is between the upper and lower edge of the beam) are independent of the length of the cathode in the z-direction and conform to and can be calculated from the following parametric equations:

where E is the field in the beam at any point y above the x-z plane and has a component only in the y direction, and t is a parametric variable common to the three equations, V is the potential in the beam flow at point y, and m is the component of w in the y direction and is equal to to sine 0. All the Equations 7, 8 and 9 are related to each other by the parameter t.

Equipotential lines within the beam are parallel to the cathode surface and the values for these parallel equipotential lines are the same as the values for the corresponding equipotential lines outside of the beam as they intersect with the internal beam equipotential line at the upper edge of the beam.

In the planar case, the electrodes found by Equations 1, 2 and 3 as plotted in FIGS. 2, 3, 4 and 5 will maintain the fields expressed by Equations 7, 8 and 9 within the beam.

In the axisymmetrical case these internal fields are still the required fields (Equations 7, 8 and 9) to be produced within the beam near the cathode surface.

For design purposes of an axisymmetrical gun, the premise is made that the electric fields at and near the cathode are the ones of chief significance. Thus, if the fields in the neighborhood of the cathode were correct, the current density in the cathode region would be very nearly that of the predicted form (uniform), but the electron trajectories far from the cathode would be somewhat different than predicted. The electrons which are furthest out radially from the cathode have, however, already been accelerated up to velocities corresponding to perhaps as much as half the anode potential. The result is that the effect of their space-charge on the fields at the cathode is small in comparison with the space-charge fields of slowly moving electrons close to the cathode. Thus, the space-charge effects near the cathode would not be greatly altered by some change in the trajectories at points radially far from the cathode.

Therefore the axisymmetric gun design procedure will involve making slight changes in the anode geometry of an equivalent planar gun to produce the desired electric field near the cathode electrode of the axisymmetric gun. The procedure for the electrode design of an axisymmetric gun employing the invention preferably should take one of the following preferred forms although one skilled in the art can after reading the teachings of this invention develop other forms. In one of the preferred forms, an equivalent planar gun using the required current density at the cathode and the same angle between the cathode surface and the magnetic field as the axisymmetrical gun is first designed using the above Equations 1, 2, 3, 4, 5, and 6. For such a planar gun, the electric field in the cathode region may be regarded as being composed of two parts: the field due to the space-charge and its image in the cathode and in the other electrodes, and the field due to the electrodes. The space-charge field for the equivalent axially symmetric gun in the neighborhood of the cathode is assumed to be the same as that for the planar gun.

The actual field between the electrodes in the absence of space-charge is a complex function and is best determined by making an electrolytic tank model of the planar gun. Referring to FIG. 6, the plan view of a typical electrolytic tank 43 is shown. The tank contains a suitable liquid electrolyte 44 having its liquid surface parallel to the bottom of the tank. Members 11', 12, 13' and 39' represent models of the cathode, front inner focusing electrode, rear focusing electrode, and anode respectively of the planar gun. Now the electric field near the cathode ll' can be measured and recorded. Referring to FIG. 7, a model for the axisymmetrical gun is approximated tilting the tank 43 of FIG. 6 until the liquid surface by the electrolyte 44 forms an angle D with the bottom of the tank and a waterline 46 is formed on the bottom to represent and correspond to the axis of the axisymrnetrical gun. The angle D is usually between 5 and 10 and is readily determined by a technician skilled in taking measurements and operating a tank of this type. Members 11, 12, 13 and 39' are positioned in the tank 44 with reference to the water line 46. Member 11' being the cathode is disposed at an angle 0 to the waterline 46, assuming the magnetic field is parallel to the tubes longitudinal axis, to approximate its frusto-conical surface and the front electrode 12 is parallel to the waterline as it is parallel to the magnetic field. Member 39' being the anode is moved away from the members 11', 12', and 13' until the same fields are measured near the cathode in the tilted tank as were measurements in the level tank of FIG. 6. Dotted line 39" (FIG. 6) represents approximately in what relationship to the other members the member 39 is displaced to form the same fields near the cathode in the axisy'mmetrical design as in the planar design. The tilted model now is used to form a scaled pattern for the axisymmetric gun electrode geometry. It turns out that the tilted model results in its anode electrode being moved slightly radially outwardly from the previous determined equivalent planar design anode electrode position.

The above process may be shortened and the gun design carried out analytically in another preferred method. Referring to FIG. 8 where a line schematic representation of the axisymmetric electron gun is shown, the cathode is represented by line 47, the inner focusing electrode by line 48, the conical focusing electrode by line 49, the anode by curve line 50, the axis of the gun is line 51 while dotted lines 52 represent the edges of the beam. Over most of the electron trajectory, electron flow is noted to be parallel to the cathode or at a very small angle to the cathode, and also the ratio of variation of the potential along the trajectory is noted to be small. Consequently, at a position 1, a small length Az of the beam, the anode, and the cathode could be regarded as being a short length of concentric cylinders. The field E at any radius r from the axis in absence of a beam and assuming no edge effected is:

E=V/d where d is the actual distance normal to the cathode (z-axis) at 1 between the anode and cathode taken from the equivalent planar gun design as found in FIGS. 25. Both guns are analyzed at the same 2 position and as before the fields near the cathode of the axisymmetrical gun are assumed to be the same as in the planar gun, therefore, Equations 10 and 11 are equated to each other giving:

T rlog 1 1 log l-d (11a) The value for r the radial position of the new anode, can now be calculated for most all values of d by inserting the value r for r in Equation 11a where r is the outside radius of the beam. The fields in the region between the frusto-conical cathode and the outside radius r of the beam should be substantially similar to the same region within the planar gun. This procedure gives an anode design which is in close agreement with the results of the electrolytic tank design. This analytical procedure can also be used for finding the shape and location of the anode from the inner focus electrode 12, but now r is the radius of the inner focus electrode. This procedure is accurate except very near the cathode. However, such a simplified analytical procedure breakdown entirely over the rear section of the cathode away from the electron exit region or approximately the rear quarter-region of the cathode as substantially represented in FIG. 1 by region I between the parallel lines.

The rear focus electrode geometry is reasonably approximated from the planar gun design since the zero potential electrode at the rear of the cathode is only of great importance in the immediate neighborhood of the cathode and sufiicient accuracy is obtained by using the zero potential electrode of the planar design.

The analytical design procedure for obtaining the position of the anode for the axisymmetrical gun, has proven in practice to yield results which are as accurate, if not more accurate, than may be obtained in an electrolytic tank. This is because of the fact that without great care in operating the tank, an electrolytic tank is not a very accurate analog device for measuring electric fields.

The gun design thus far described yields a beam at its exit which has strong components of radial field both at the inner and outer edges of the beam. Such a beam would possibly be suitable for use in an injected beam, cylindrical magnetron. However, if a hollow beam for use in a traveling wave tube or klystron is required, the beam is preferably projected into a field free or almost field-free drift region. Therefore, a suitable transition region is provided between the exit of the gun and the entrance of the drift tube 41.

In designing the transition region, the form of the beam in the drift tube region is first considered. If one assumes that the beam in the drift tube region is flowing parallel to the axis of the drift tube and its diameter is constant, then electrons on the inside of the beam experience no radial focusing due to space-charge. Consequently, to remain in equilibrium, they must experience no radial forces due to the magnetic field, and their velocity component must be zero. Referring to FIG. 1, and assuming the beam remains laminar throughout its path, Buschs theorem states that the inside electrons, which have been emitted from the point of minimum radii (a) on the cathode, lie on a cylinder having the same radius as the minimum radius of the cathode. The outer electron of the beam at radius r is acted upon by the space-charge due to the electrons in the rest of the beam within r These forces are balanced by the sum of the centrifugal force due to rotation of the electrons around the axis and the inward force due to the magnetic field. Then for electrons emitted from a point on the cathode at maximum radius b from the axis, Buschs theorem states that the angular velocity of the electron o is:

Then for beam equilibrium the following expression holds, from which r is calculated:

where O is the charge per unit length of the beam. In practice for a thin beam, this relationship states that the thickness of the beam will be the sum of the Brillouin thickness for the same value of O and the radial thickness of the cathode b-a. For equilibrium, the outer electrons in the beam are preferably contained at a radius greater by roughly the Brillouin thickness than the outer radius of the cathode.

Typical values of magnetic field are from two to three times the Brillouin field for a beam of thickness (ba) and inner radius r The resulting beam thickness is equal to (l1-a+s) where s is the Brillouin thickness for the actual field used. Now s varies as 1/8 therefore, the beam thickness 1 is:

where k is the ratio of magnetic field B as used to the Brillouin magnetic field for a beam of thickness (b--a).

At the exit of the gun, both the inner radius 1' and the outer radius r of the beam are greater than the required radii of the final beam, because of the presence of the radial electric field in the gun. If the radial electric field is slowly tapered from the exit of the gun to the required value in the drift region, the beam itself will also decrease in diameter so that at any point in the beam E mB qS, where is found from Buschs theorem using the above Equation 12. E, is the actual electric field at radius r. In order to minimize beam rippling the rate of change of the radius of the beam should be slow, the taper of the electric field occurring in a distance comparable to, or greater than, the cyclotron wavelength. In practice, the drift tube 41 (FIG. 1) is essentially a continuation of the anode 39 of the gun, and the inner focus electrode 12 of the gun in the exit region is preferably gradually tapered to zero diameter.

Referring to FIG. 9 there isshown a portion of another embodiment of the electron gun forming the present invention wherein the gun had a modified inner focusing electrode 12" by which the above mentioned taper in the electric field is produced. The same items in FIGS. 1 and 9 are designated with like numbers. Electrode 12" has a cylindrical surface 53 adjacent the cathode 14 and substantially parallel to the magnetic field while its other end is tapered inwardly towards the axis and away from the beam. Instead of making this surface smooth as the inner surface on the anode 39 as shown in FIG. 1, for economy-of construction the end portion consists of two conical surfaces 54 and 55 positioned progressively forward wherein the apex angle of surface 54 is larger than the apex angle of surface 54. This shape approximates the above mentioned transition to Zero diameter.

A gun was made using the teachings of this invention which gun was required to have the design parameters as shown in Table I:

. 7 Table I Perveance, micropervs 10 Voltage, kilovolts 1.5 Current, amps 0.581 Current density at cathode J =0.088 amp./cm. Half angle of cathode cone, 0:4". Area convergence of beamzcosec 0% 14. Beam ID (inside diameter), inches 0.5 Cathode areas, cm. 6.6 Cathode length, inches 0.6 Approximate beam thickness, inches 0.042 Brillouin magnetic field for drift tube: Diameter of 0.75 inch, gauss 192 Chosen magnetic field, gauss 542 Normalizing factors -;%=1.92 l0 and The gun was tested and it had a perveance of 10.8 micropervs. and a current emission density that was uniform to within 10%.

Also other guns have been constructed using the above teachings with ratios of cathod length to diameter of 2.4:1 and 4:1. These guns have been tested and found to give perveances to about 10% of the design value with current emission densities uniform also to within 10%.

The main object of the above description was to teach methods for determining the shape of gun electrodes so that the field and equipotential lines within the hollow beam substantially conform to Equations 7, 8, and 9 so that the object of the invention may be accomplished. The cathode electrode may have other forms such as, for example, the cathode surface 11 may be cylindrical. For such a case the magnetic field is preferably outwardly barreled through the cathode surface and thus non-parallel to the tube axis. Also, the anode 39 may have various forms and for these forms, the front focus electrode 12 is preferably modified.

Referring to FIG. 10, an alternate anode structure comprises a plurality of metal rings 56-61 all at the same potential with respect to-the cathode 14 which potential is supplied by a suitable DC. power supply 62. Although only six rings are shown more or less rings could be used without departingfrom the teachings of the invention. Rings 56-61 approximate the bell-shaped anode 39 of FIG. l'so that although the fields near the anode are distorted and non-bell-shape, the fields near the cathode 14 are bell-shape whereby a uniform cathode emission is produced. The diameters of the rings 56-61 are related to their axial position in a non-linear manner so that the smallest ring 56 is at one end and the largest ring 61 is at the other end.

Referring to FIG. 11, another embodiment of the bellshaped anode comprises preferably equal diameter metal rings 63-68 which are preferably spaced uniformly in an axial direction. These rings 63-68 unlike rings 56-61 (FIG. 10) are at a progressively increasing potential with respect to the cathode 14 and to each other, with ring 68 being at the lowest potential difference with respect to the cathode 14 and ring 63 being at the highest potential difference with respect to the cathode. Suitable DC. power supplies 71-76 provide the necessary potential to the electrodes and rings. Since the rings 63-68 are uniformly spaced and the power supplies 71-76 are in series, the electromotive forces supplied by each power supply 72-76 decreases non-linearly with axial length so that the equipotential line produced near the cathode are bell-shaped. If power supplies 72-76 should supply equal electromotive force then the axial spacing between rings should be non-uniform with the spacing between each successive rings 63-68 increasing in a non-linear manner with axial length in that the spacing between ring 63 and 64 is the largest. This anode arrangement also produces bellshape'd equipotential lines near the cathode 14. Other combinations of rings and power supplies can be chosen to form an equivalent bell-shaped anode so that bellshaped equipotential surfaces are produced near the cathode to provide uniform cathode emission;

Referring to FIG. 12, there is shown what is commonly called an inside out gun because the cathode 77 is located exterior of an anode 78. A rear focusing electrode 79 is frusto-conical but its largest diameter is now located near the cathode, and front focusing electrode is now a ring 81, with a cylindrical portion adjacent the cathode 77. A heater 82 is located outside of the cathode 77. The inside emission surface 83 of the cathode 77 is also frusto-conical so that the axially parallel magnetic field B forms an angle 0 with the cathode surface 83 (arrow B is also the axis about which the gun is symmetrical). A drift tube 84, at the same potential or at more positive potential than the anode, is disposed next to the front focusing electrode. Electrodes 77, 79, 81 and 84 are conveniently supported by suitable members (not shown) while the anode is preferably supported on a rod 85 extending axially from the rear end of the gun.

The gun forms a hollow beam 85 which has an outer radius that becomes larger within the drift tube 84 until the outer radius is about the same radius as the front radius of the cathode 77 (somewhat similar to the embodiment described in FIG. 1). Therefore, the radius of the drift tube 84 should be slightly larger than the out side radius of the beam 85.

Half partial cross section views of both the regular and inside out axisymmetrical guns are somewhat similar as one can observe from FIGS. 1 and 12 as delineated by lines 1313 and 14-14 in each figure, respectively.

The actual positions of the electrodes in the inside out gun are determined from Equationsl, 2, and 3 and from the graphs shown in FIGS. 2, 3, 4 and 5. As in designing the regular axisymmetrical design, the tank model of the electrodes are placed in the electrolytic tank 43 as shown in FIG. 6 and the electric fields are measured between members 11' and 39'. However, the tank 43, for the inside out gun, is tilted in the opposite direction than for the regular gun design, as shown in FIG. 7, so that the waterline 46, which represents the tube axis, is disposed in between anode member 39 and the side of the tank. In making the field measurements, the anode member 39 should now be moved towards the cathode member 11, for the inside out gun, in order to obtain the same electric field near the cathode 11' as were measured in the planar gun tank model.

Also, as in the regular gun, the position of the anode electrode for the inside out gun can be approximated analytically, but Equation 11a is now rewritten as follows:

1', log r /r =d (15) where r, is the inside radius of the beam while r 1' and d represent the same functions as in Equation 11a.

Thus, one difference between the positions of the electrodes of the regular axisymmetrical gun and the positions of the electrodes of the inside out axisymmetrical gun, as compared to the planar gun, is that the anode is moved away from the cathode to make the regular axisymmetrical gun whereas the anode is moved closer to the cathode from the planar design gun to make the inside out gun.

Since many changes could be made in the above construction and many apparently widely different embodiments of this invention could be made without departing from the scope thereof, it is intended that all matter contained in the above description or shown in the accompanying drawings shall be interpreted as illustrative and not in a limiting sense.

What is claimed is:

1. An electron gun comprising a cathode having an elongated electron-emissive surface, a bell-shaped anode means disposed axially coextensive with said surface, said bell-shaped anode means providing bell-shaped tubular equipotential surfaces between the anode and cathode, said bell-shaped tubular equipotential surfaces having a non-linear variation in diameter along the gun axis, and means establishing a beam confining magnetic field disposed at an angle with said cathode surface and threading through said surface.

2. The electron gun of claim 1 wherein said angle between the magnetic field and said cathode surface is less than 10.

3. The electron gun of claim 1 wherein said bell-shaped anode means is geometrically limited to a plurality of axial spaced rings, said rings having the same potential and different diameters, said rings being disposed concentric with said cathode with the largest diameter ring at one end and each successive ring having a smaller diameter, and the rate of change of diameters in relation to axial length being non-linear whereby bell-shaped equipotential lines are formed adjacent to the cathode.

4. The electron gun of claim 1 wherein said bell-shaped anode means is geometrically limited to a plurality of spaced rings having equal diameters, each ring starting with the ring disposed on the end remote from the beam having a potential greater than the next adjacent ring, the rate of change of the potential of said rings relative to axial length is non-linear whereby bell-shaped equipotential lines are formed adjacent to the cathode.

5. An electron gun comprising, a cathode having an elongated electron-emissive surface, a frusto-conical electrostatic focusing electrode disposed at one end of said surface, and forming an angle larger than 90 with said surface and a bell-shaped anode disposed axially coextensively with said surface.

6. An electron gun comprising a cathode having an elongated electron-emissive surface, an anode disposed axially coextensively with said cathode surface, an electrostatic focusing electrode disposed at one end of said surface and forming an angle larger than with said surface, said anode being adapted and arranged such that bell-shaped equipotential lines are formed adjacent to the cathode, said gun including means for forming a magnetic field.

7. The electron gun of claim 6 wherein means are provided for forming a magnetic field disposed within said gun to form an angle with and threading through said surface.

8. The electron gun of claim 6 wherein said anode is disposed outside said cathode, and said electrostatic focusing electrode surface forms an angle with said cathode surface which angle is between and 9. The electron gun of claim 7 wherein said cathode surface is substantially frusto-conically shaped, said electrostatic focusing electrode having a frusto-conical surface, and said magnetic field being disposed axially parallel to the longitudinal axis of revolution of said cathode surface, the larger diameter end of said cathode surface being disposed adjacent the smaller diameter end of said frusto-conical electrostatic focus electrode surface and forming an angle which is between 115 and 160 therebetween.

10. An electron gun comprising a cathode having an elongated electron-emissive surface, an anode defining a surface spaced from and facing said electron-emissive surface disposed axially coextensively with said cathode surface, a rear electrostatic focusing electrode disposed at one end of said cathode surface forming an angle larger than 90 with said surface, a front electrostatic focusing electrode disposed at the other end of said cathode, and means for forming a magnetic field forming an angle with said cathode surface and threading said cathode surface.

11. The electron gun of claim 10 wherein said rear electrostatic focusing electrode has a frusto-conical surface forming an angle with said cathode surface which angle is between 115 and 160, and said front electrostatic focus electrode has a surface disposed substantially parallel with the mangetic field.

12. The electron gun of claim 11 wherein said cathode surface has a frusto-conical shape with the larger diameter end thereof disposed adjacent said frusto-conical surface of said rear electrostatic focusing electrode, and said magnetic field being directed parallel to the axis of revolution of said cathode surface.

13. The electron gun of claim 12 wherein said anode is geometrically limited to a bell-shape form.

14. An electron gun comprising a cathode having an elongated electron-emissive surface, an anode disposed axially coextensive with said cathode surface, a rear focusing electrode disposed at one end of said cathode surface forming an angle lying between 115 and 160 with said surface, a front focusing electrode disposed at the other end of said cathode, and means for forming a magnetic field forming an angle with said cathode surface and threading said cathode surface, said front focusing electrode having a surface disposed substantially parallel with the magnetic field, said cathode surfoce having a frusto-conical shape with the larger diameter end thereof disposed adjacent said frusto-conical surface of said rear focusing electrode, and said magnetic field being directed parallel to the axis of revolution of said cathod surface, said bell-shaped anode being geometrically limited to a bell-shape form and having a surface facing said cathode surface and having a largest diameter disposed at one end and a smallest diameter at the other end, said anode surface having a plurality of diameters disposed between said end diameters which plurality of diameters become progressively smaller non-linearly along the axial length of the anode from said one end to said other end.

15. The electron gun of claim 14 wherein said front focusing electrode includes a tapered surface portion, said tapered surface being disposed at an end of said 13 front focus electrode remote from said cathode, and sloping away from said anode.

16. An electron gun comprising a cathode having a frusto-conical electron-emissive surface, a frusto-conical electrostatic focusing electrode disposed at one end of and coaxial with said cathode surface, and a bell-shaped anode disposed concentric with and exterior of said cathode, said bell shaped anode having a largest diameter end disposed at the same end of the'gun as said frustoconical electrostatic focusing electrode, said frusto-conical electrostatic focusing electrode surface disposed at an angle to said cathode surface which angle is between 115 and 160, said frusto-conical electrostatic focusing electrode being disposed with its small diameter end adjacent the large diameter end of said cathode surface, and means for forming a magnetic field through said gun which is substantially parallel to the axis of revolution of said frustoconical cathode surface.

17. An electron gun comprising a cathode having a frusto-conical electron-emissive surface, a frusto-conical focusing electrode disposed at one end of and coaxial with said cathode surface, and a bell-shaped anode disposed concentric with and exterior of said cathode, said bell-shaped anode having a largest diameter end disposed at the same end of the gun as said frusto-conical foo-using electrode, said frusto-conical focusing electrode surface disposed at an angle to said cathode surface which angle is between 115. and 160, said frusto-conical focusing electrode being disposed with its small diameter end adjacent the large diameter end of said cathode surface, and means for forming a magnetic field through said gun which is substantially parallel to the axis of revolution of said frusto-conical cathode surface, said bell-shaped anode being geometrically limited to an electrode geometry having a largest inside diameter disposed at one end and a smallest diameter at the other end, said anode having a plurality of inside diameters disposed between said end diameters which plurality of diameters becomes progressively smaller non-linearly with axially length of the anode from said one end to said other end, whereby bell-sha-ped equipotential lines are formed adjacent to the cathode.

18. An electron gun comprising, a cathode having an elongated electron-emissive surface symmetrical about an axis, means establishing a magnetic field disposed at an angle with said cathode surface, and means for forming a hollow electron beam originating from said cathode surface where the fields in the beam and the potential of the beam conform to the following parametric equawhere y is a distance normal to the cathode surface, E is the electric field at point y, V is the potential of the beam at point y, n is equal to minus the ratio of electron charge to electron mass (-e/ m), L, is the current emission density at the cathode, w is 1; times the magnetic field, m is to times the sine of the angle the magnetic field makes with the cathode, s is a constant and equal to 8.854 farads per meter in mks. units, and t is a parametric function.

19. The electron gun of claim 18 wherein said means for forming said hollow electron beam comprises a tubular anode concentric with said cathode surface, and a frusto-conical focusing electrode disposed coaxial with and at the far end of said cathode surface remote from said beam.

20. The electron gun of claim 18 wherein said means for forming said hollow electron beam comprises a bellshaped anode concentric with and exterior of said cathode surface and disposed with the far end of said anode remote from the beam having a larger diameter than the other end of the anode.

21. An axisymmetric electron gun comprising, a tubular cathode surface substantially symmetrical about an axis, means for establishing a mangetic field disposed at an angle 0 with said cathode surface, and a bell-shaped anode disposed substantially coaxially of and axially coextensive with said cathode surface, said bell-shaped anode being dimensioned so that the equipotentials produced by said anode, in the vicinity of a hollow electron beam generated by said gun, said vicinity being radially limited to distances external to the outer boundary and internal to the inner bounadry of said hollow beam which radial distances as measured from the respective inner and outer beam boundaries are limited to the beam thickness, substantially conform to the equipotential lines of the corresponding one of FIGURES 2, 3, 4 and 5 when the equipotentials of said figures are compensated for the particular axisymmetric case.

22. An electron gun comprising a tubular cathode surface symmetrical about an axis, means establishing a magnetic field disposed at an angle with said cathode surface, a bell-shaped anode disposed concentric with and interior of said cathode surface, said bell-shaped anode being disposed at a variable distance from said cathode surface, said variable distance being determined so that the equipotential line of the anode falls in an area on the graphs of FIGS. 2, 3, 4 and 5 which area is on one side of the equipotential lines that represents the equipotential line of the anode in a normalized potential value in a normalized Y-Z coordinate system, and said one side being of the near side of said one equipotential line to the origin of the co-ordinate system.

23. An electron gun comprising a tubular cathode symmetrical about an axis, means establishing a magnetic field disposed at an angle with said cathode, and a bell-shaped anode concentric with and exterior of said cathode, said bell-shaped anode being related to any one of the curves of an equipotential line as found from the graph in FIGS. 2, 3, 4 and 5 which line corresponds to the normalized potential of the anode in a normalized Y-Z co-ordinate system, and the radius r of said anode for a given Z value lying in the forward three-quarter portion of said cathode being related to the actual distance d between the Z-axis and said one equipotential curve on said graph at said given Z value by the equation:

where r is the outer diameter of the beam, d is the actual distance between said one equipotential line and the Z-axis as taken from the equivalent planar gun de sign of FIGS. 2, 3, 4 and 5, r is the radius of the anode and r is the radius of the cathode, all values being at the given Z value.

24. An electron gun comprising a tubular cathode symmetrical about an axis, means establishing a magnetic field disposed at an angle with said cathode, and a bell-shaped anode concentric with and interior of said cathode, said bell-shaped anode being related to any one of the curves of an equipotential line as found from the graph in FIGS. 2, 3, 4 and 5 which line corresponds to the normalized potential of the anode in a normalized Y-Z co-ordinate system, and the radius 1- of said anode for a given Z value lying within the forward threequarter portion of said cathode being related to the actual distance d between the Z-axis and said one bell-shaped equipotential curve on said graph at said given Z value by the equation:

1', log g=d where r, is the inner diameter of the beam, at is the actual distance between said curve and the Z-axis, r is the radius of the anode and r is the radius of the cathode, all values being at the given Z value.

25. A method for forming a hollow beam having a high perveance comprising forming a magnetic field at an angle with a tubular cathode, forming an electric field component normal to the tubular cathode, and within said hollow beam said field having a form which conforms to the following parametric equations:

where y is a distance normal to the cathode surface, E is the field at point y, 1 is equal to minus the ratio of electron charge to electron mass (e/m), I is the current emission density at the cathod, V is the potential of the beam at point y, w is '1 times the magnetic field, to is w times the sine of the angle the magnetic field makes with the cathode, s is a constant and equal to 8.854' 10 farads per meter in m.k.s. units and tis a parametric function.

26. An electron gun' comprising, a cathode having an elongated electron-emissive surface symmetrical about an axis, an anode electrode having an elongated axial extent and coaxially disposed with respect to said cathode, means" establishing an axial magnetic field disposed at an angle with said cathode surface, and front electrostatic focus electrode having an elongated tubular shaped surface configuration, said front focus electrode being coaxially disposed with respect to said cathode, said front focus electrode having its tubular shaped surface disposed substantially parallel to said magnetic field.

27. The electron gun defined in claim 26 wherein said front electrostatics focus electrode includes a tapered tubular surface sloping away from the electron beam formed by said gun.

28. An electron gun comprising, a cathode having an elongated electron-emissive surface electrostatic anode means disposed concentric with said cathode surface, means establishing a magnetic field disposed at an angle with said cathode surface, said electrostatic anode means producing bell-shaped tubular equipotential surfaces adjacent said cathode, said tubular bell-shaped equipotential surfaces having a non-linear variation in diameter along the gun axis.

29. An electron gun comprising a cathode having an elongated electron-emissive surface, a bell-shaped anode disposed axially coextensive with said surface, and means establishing a beam confining magnetic field disposed at an angle with said cathode surface and threading through said surface, said bell-shaped anode being geometrically limited to a tubular surface having 3. largest diameter disposed at one end a smallest diameter at the other end, said anode surface having a plurality of diameters disposed between said end diameters which plurality of diameters become progressively smaller nonlinearly with axial length of the anode from said one end to said other end whereby bell-shaped equipotential lines are formed adjacent to the cathode.

References Cited by the Examiner UNITED STATES PATENTS 2,632,130 3/1953 Hull. 2,760,101 8/1956 Reverdin 315--3.5 2,843,776 7/1958 Tien. 2,936,393 5/1960 Currie et al 315-3 GEORGE N. WESTBY, Primary Examiner. c. o. GARDNER, R. SEGAL, Assistant Exmniners. 

1. AN ELECTRON GUN COMPRISING A CATHODE HAVING AN ELONGATED ELECTRON-EMISSIVE SURFACE, A BELL-SHAPED ANODE MEANS DISPOSED AXIALLY COEXTENSIVE WITH SAID SURFACE, SAID BELL-SHAPED ANODE MEANS PROVIDING BELL-SHAPED TUBULAR EQUIPOTENTIAL SURFACES BETWEEN THE ANODE AND CATHODE, SAID BELL-SHAPED TUBULAR EQUIPOTENTIAL SURFACES HAVING A NON-LINEAR VARIATION IN DIAMETER ALONG THE GUN AXIS, AND MEANS ESTABLISHING A BEAM CONFINING MAGNETIC FIELD DISPOSED AT AN ENGLE WITH SAID CATHODE SURFACE AND THREADUBG THROUGH SAID SURFACE. 